Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Computational Commutative Algebra 1
Computational Commutative Algebra 1
On efficient computation of grobner bases
On efficient computation of grobner bases
F5C: A variant of Faugère's F5 algorithm with reduced Gröbner bases
Journal of Symbolic Computation
Signature-based algorithms to compute Gröbner bases
Proceedings of the 36th international symposium on Symbolic and algebraic computation
A generalized criterion for signature related Gröbner basis algorithms
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Modifying Faugère's F5 algorithm to ensure termination
ACM Communications in Computer Algebra
New algorithms for computing groebner bases
New algorithms for computing groebner bases
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The F5 algorithm [8] is generally believed as one of the fastest algorithms for computing Gröbner bases. However, its termination problem is still unclear. The crux lies in the non-determinacy of the F5 in selecting which from the critical pairs of the same degree. In this paper, we construct a generalized algorithm F5GEN which contain the F5 as its concrete implementation. Then we prove the correct termination of the F5GEN algorithm. That is to say, for any finite set of homogeneous polynomials, the F5 terminates correctly.